1. The Product Rule

2. SUMMARY
Otherwise use the product rule: If
where u and v are both functions of x
To differentiate a product:
Check if it is possible to multiply out. If so, do it and differentiate each term.

3. Let
e.g.
and
Remove common factors:

4. We can now differentiate all of the following:
A simple function could be like any of the following:
We differentiate them term by term using the 4 rules for
The multiplying constants just “tag along”.
simple functions,
products and

5. Decide how you would differentiate each of the following ( but don’t do them ):
Product rule
Chain rule
This is a simple function
For products we use the product rule and for functions of a function we use the chain rule.

6. It can be tricky to distinguish between products and functions of a function.
If you do have difficulty try the following:
Assume you have a product.
Then, you must have 2 factors ( at least ).
If you can’t then it isn’t a product.
Try to split up the function into one function multiplied by another.